Forget the calculator! This 10-mathematical trick you do not teach in school.
Mathematics is not so complicated science as it might seem at first glance. There are many secrets that allow you to do very complex calculations in his mind. If you find it difficult to calculate how much tip to leave the waiter or difficult to split a restaurant bill at all, these 10 tricks just for you. And by the way, it's a great workout for your brain!
How to get 15% of any number of
You must first calculate 10% of it, and then divide that number by 2 and add up these numbers.
Example: 15% of the 358
1. Find the 10% - 35, 8.
2. Find half of the 35, 8 - is 17, 9.
3. Heap 17, 9 to 35, 8, and you get 53, 7.
multiplication "3 in 1" in the mind
You have no idea how easy it is. You just need to divide a large task into several small.
Example: 450 × 6
1. Break the number 450 into two simpler: 400 and 50.
2. Multiply 400 6 50 and 6 separately (300 and 2400).
3. Fold the resulting number (2700).
Squaring double digits
With this trick you will be squaring two-digit numbers very quickly. All you need - divide the number by two and get an approximate answer.
Example: 53 ^ 2
1. Subtract 3 from 53 to 50 receive and add 3 to 53, to obtain 56.
2. Multiply the two numbers using the previous council (50 × 56 = 2800).
3. Heap square of the number, the value of which you increase or decrease 53 (2800 + 3 ^ 2 = 2809).
The secret is that when squaring two-digit numbers, you need to turn them into numbers that multiply much easier, as we did with the number 53.
Squaring numbers ending in 5
With this mathematical operation, things are even simpler. Take the first digit of the number that you are squared. Multiply it by the same number plus 1. Then add at the end of 25.
Example: 85 ^ 2
1. Multiply 8 to 9 and you get 72.
2. Add to the number 25 and you get 7225.
The division into the number-one
The division in the mind - it is a skill that you need a little every day.
Example: 589: 7
1. It is necessary to find approximate answers, multiplying such number 8, which give the final result (= 80 7 × 560 7 × 90 = 630). The answer is more than 80.
2. Subtract 560 from 589. After receiving the number 29, divide it by 7 and you get 4 with remainder 1.
3. A - 84 1
The answer, of course, is not the most accurate, but even this response to you will be enough, for example, to pay in a restaurant.
How to quickly find the cube roots of numbers
To find the cube root of any number, you need to learn the cubes of numbers from 1 to 10:
Knowing them by heart, you can easily find the cube root of any number.
Example: cube root of 39,304
1. Take the amount of thousands of (39) and found, between which it is numbers (27 and 64). This means that the first digit in the answer - 3, and the answer lies in the range of 30.
2. Each digit from 0 to 9 will appear in the cube roots of numbers from 1 to 10 only once.
3. Since the last digit in this case - 4, which means that the last digit of the answer is 4 because its cubic root of the latter figure 4.
4. A - 34.
To find out how many years you can double your money, divide the number 70 on the annual interest rate.
Example: as tenderly years to double the money with an annual interest rate of 17%.
70: 17 = 4, 1 year
To find out how many years you will be able to triple your money, you need to divide the number 110 on the annual interest rate.
Example: how many years it is necessary to triple the money with an annual interest rate of 20%.
110: 20 = 5, 5 years
The magic number 1089
But this trick will surprise anyone! Think of any three-digit number, digits are in descending order, for example, 642 or 864. Then, write it in reverse order, and subtract it from the original number. To this number add the same number, but spelled backwards. What do you get? 1089?
You probably often seen such a trick conceived by any number. Multiply it by 2. Add 12. Divide the sum by 2. Subtract from it the original number.
You got 6, is not it? Whatever you put forth, you still get 6. And here's why:
2. 2 +12
3. (2 + 12): 2 = +6
4. +6 -
This is the basic rules of algebra are now such tricks will not surprise you.
I wonder why we do not teach it in school. It turns out that the multiplication of a column outdated and these secrets is much better than most of the things we were taught in math class.
Show your friends how you can do complex mathematical calculations in his mind!